In coherent optical communication, large-capacity transmission at tens of Gbits/s or higher is realized by compensating for distortion of a transmission signal in digital signal processing. On the transmission side, transmission characteristics of a transmission circuit can be compensated for in advance by digital signal processing. Further, on the reception side, chromatic dispersion, polarization multiplexing/separation, polarization dispersion, frequency/phase fluctuation and the like caused in an optical fiber transmission path or a reception circuit can be compensated for by digital signal processing.
In the digital signal processing, adaptive equalization for continuously adaptively performing compensation for an environment of a transmission path which changes with time is one of the most important functions. Improvement of higher compensation accuracy of the function is demanded in order to realize a larger capacity.
The compensation portion which compensates for transmission characteristics of a signal is generally configured with a digital filter, and, by setting such a tap coefficient that can offset distortion of a transmission signal, for the digital filter, it is possible to perform compensation on the transmission signal. Therefore, accuracy of the compensation depends on appropriateness of the tap coefficient. Especially, for adaptive equalization on the reception side, various algorithms are proposed.
For example, PTL 1 proposes, as a method for equalizing transmission characteristics on the reception side in an orthogonal frequency division multiplexing (OFDM) system, a method in which a butterfly type filter is used to calculate a filter coefficient of the filter from known pilot frequency data using a minimal mean square error (MMSE) method. By calculating an inverse matrix of a result of multiplication with a complex conjugate transpose of a transmission signal by Formula (7) of PTL 1, a filter coefficient for horizontally polarized wave and a filter coefficient for vertically polarized wave can be determined. Further, NPL 1 introduces a general MSE algorithm.
FIG. 8 is a diagram showing a conventional adaptive equalization apparatus. A received signal which has passed a transmission path 100 such as an optical fiber has transmission characteristics. An adaptive filter 101 is a compensation portion which compensates for the transmission characteristics and is generally configured with an FIR filter. It is possible to, by setting a tap coefficient for the FIR filter, compensate for distortion and the like caused in the transmission path 100. Further, if the transmission path 100 is thought to be a characteristic of an amplifier and the like on the transmission side, it is also possible to compensate for distortion of an output signal of the amplifier in advance.
A coefficient calculating portion 102 uses a minimal mean square error method as an algorithm for calculating the tap coefficient. An error e(n) between an output of the adaptive filter 101 and a known signal sequence (referred to as a reference signal) is expressed by the following equation:e(n)=d(n)−Y(n)=d(n)−W(n)TX(n)Here, d(n) indicates the reference signal; Y(n) indicates the output of the adaptive filter; W(n) indicates a tap coefficient of the adaptive filter; T indicates a transposed matrix; and X(n) indicates a received signal which has passed a transmission path.
In order to remove uncertainty of signs, what is obtained by averaging squared errors is set as an index MSE.MSE=E[e(n)2]=E[(d(n)−W(n)TX(n))2]
A solution of the tap coefficient of the filter when the above value is minimized is generally known as a winner solution and is determined by the following equation. Here, −1 indicates an inverse matrix.W(n)=(X(n)TX(n))−1X(n)Td(n)